Data-Driven Distributionally Robust CVaR Portfolio Optimization Under A Regime-Switching Ambiguity Set

Problem definition: Nonstationarity of the random environment is a critical yet challenging concern in decision-making under uncertainty. We illustrate the challenge from the nonstationarity and the solution framework using the portfolio selection problem, a typical decision problem in a time-varying financial market. Methodology/Results: This paper models the nonstationarity by a regime-switching ambiguity set. In particular, we incorporate the time-varying feature of the stochastic environment into the traditional Wasserstein ambiguity set to build our regime-switching ambiguity set. This modeling framework has strong financial interpretations because the financial market is exposed to different economic cycles. We show that the proposed distributional optimization framework is computationally tractable. We further provide a general data-driven portfolio allocation framework based on a covariate-based estimation and a hidden Markov model. We prove that the approach can include the underlying distribution with a high probability when the sample size is larger than a quantitative bound, from which we further analyze the quality of the obtained portfolio. Extensive empirical studies are conducted to show that the proposed portfolio consistently outperforms the equally weighted portfolio (the 1/N strategy) and other benchmarks across both time and data sets. In particular, we show that the proposed portfolio exhibited a prompt response to the regime change in the 2008 financial crisis by reallocating the wealth into appropriate asset classes on account of the time-varying feature of our proposed model. Managerial implications: The proposed framework helps decision-makers hedge against time-varying uncertainties. Specifically, applying the proposed framework to portfolio selection problems helps investors respond promptly to the regime change in financial markets and adjust their portfolio allocation accordingly.